Market Impact Decay

The temporary impact component typically follows an exponential decay pattern, where the price reverts rapidly at first and then asymptotically approaches the equilibrium. The decay constant (λ) defines the half-life of the distortion.

• Fast initial reversion: Most of the distortion dissipates within seconds to minutes
• Long tail: Residual effects can persist for hours in illiquid instruments
• Model formulation: P(t) = P_impact * e^(-λt) + P_permanent

The half-life of market impact—the time required for half the temporary distortion to dissipate—is inversely proportional to market liquidity. Highly liquid instruments exhibit near-instantaneous reversion, while illiquid assets may carry distortion for extended periods.

• Large-cap equities: Half-life measured in seconds
• Small-cap equities: Half-life measured in minutes to hours
• Fixed income: Decay varies by issue size and market structure
• FX majors: Sub-second reversion during active trading sessions

Market impact decay applies exclusively to the temporary impact component. The permanent impact—the price change reflecting new information conveyed by the trade—does not decay and represents a lasting adjustment to the asset's equilibrium value.

• Temporary impact: Transient liquidity concession that fully reverts
• Permanent impact: Information-driven price change that persists indefinitely
• Decomposition: Total impact = Temporary (decaying) + Permanent (persistent)
• Kyle's Lambda (λ): Quantifies the linear relationship between order flow and permanent price change

Quantifying decay rates requires high-frequency econometric techniques applied to tick-level trade and quote data. Common approaches include:

• Vector Autoregression (VAR): Models the dynamic interaction between trades and quote revisions
• State-space models: Separate temporary and permanent impact components using Kalman filters
• Event studies: Measure cumulative abnormal returns post-trade relative to a benchmark
• Hawkes processes: Capture self-exciting dynamics where trades trigger further trading activity

Understanding decay rates enables optimal execution scheduling. Algorithms can time child order submissions to coincide with expected reversion windows, minimizing the cumulative impact of a large parent order.

• Spacing logic: Delay subsequent slices until prior impact has partially decayed
• Adaptive participation: Increase aggression when decay is fast, reduce when slow
• Market making: Provide liquidity during decay phases to capture spread while distortion reverts
• Alpha preservation: Faster decay means less information leakage and better signal retention

The transient price concession required to attract liquidity for a trade, which reverses after the order is completed. This is the component of market impact that decays. It represents the compensation paid to liquidity providers for the risk of holding inventory during the execution period. Unlike permanent impact, which reflects new information, temporary impact is a purely mechanical cost that dissipates as the order book replenishes.

• Key distinction: Reverses fully after trade completion
• Duration: Typically seconds to minutes in liquid markets
• Modeling: Often captured by the resilience parameter in propagator models

The speed at which the limit order book replenishes itself after a trade removes liquidity. High resilience means rapid decay of temporary impact; low resilience means price distortions persist. This parameter is critical in the Obizhaeva-Wang model and other microstructure frameworks.

• High resilience: Tightly bid markets with many market makers
• Low resilience: Illiquid instruments where gaps remain unfilled
• Measurement: Estimated via the exponential decay rate of price deviations

The lasting change in an asset's equilibrium price caused by a trade that conveys new information to the market. This component does not decay because it reflects a genuine reassessment of fundamental value. The total market impact of a trade is the sum of temporary impact (which decays) and permanent impact (which persists).

• Information-based: Driven by adverse selection and signaling
• Linear models: Kyle's Lambda relates order flow to permanent price change
• Empirical split: Typically 50-70% of total impact is permanent in equity markets

A class of market impact models that decompose price changes into a transient component (which decays) and a permanent component. The propagator function describes how past trades continue to influence the current price, with the decay kernel capturing the temporal dissipation of temporary impact.

• Key insight: Impact is not instantaneous but propagates through time
• Calibration: Uses tick-level trade and quote data to estimate decay functions
• Advantage over Almgren-Chriss: Captures realistic non-linear decay patterns

The ratio of buy-side to sell-side liquidity resting in the limit order book. After a large trade depletes one side, the resulting imbalance creates the temporary price distortion that subsequently decays as new orders arrive. The rate of decay is directly proportional to how quickly this imbalance normalizes.

• Pre-trade signal: High imbalance predicts adverse price movement
• Post-trade recovery: Imbalance normalization = impact decay
• Real-time metrics: Volume-Synchronized Probability of Informed Trading (VPIN) tracks persistent imbalances

The time window over which an algorithm slices a parent order to minimize the combined costs of market impact and timing risk. Longer horizons allow temporary impact to decay between child orders, reducing total cost. The optimal schedule balances this decay benefit against the risk of adverse price movements during the extended execution.

• Almgren-Chriss framework: Solves for the optimal decay-exploiting schedule
• Faster decay → shorter optimal horizon: Less need to wait for dissipation
• Slower decay → longer optimal horizon: Must space trades further apart